# Balancing Necessity and Fallibilism: Charles Sanders Peirce on the Status of Mathematics and its Intersection with the Inquiry into Nature

An interest in Charles Sanders Peirce and pragmatist thought in general emerged in the United States in the middle of last century to exert a powerful influence on a generation of American philosophers educated in the 1940s and 1950s, including Abner Shimony, whose thought is the occasion for this paper. Those threads in Peirce's work related to developing a scientifically informed worldview and metaphysics were the natural influences on Abner and this paper will begin by briefly reviewing a number of these threads and their influences in his writings. This sets the scene for the main project of the paper, an earlier historical project on a related aspect of Peirce's thought—his understanding of mathematics and its place in the description of nature. Mathematics was a foundational discipline for Peirce, one with qualities of necessity and certainty, features that stand in interesting contrast and tension to Peirce's view of an evolving nature which is governed by chance and our knowledge of which is always fallible and thus open to revision. Exploring these issues reveals deep background beliefs structuring Peirce's thought. The paper concludes in the contemporary realm with the speculation that due to the scientific developments of the 20th century, aspects of Peirce's work that formed a vision for a scientific metaphysics for earlier generations may be less relevant now. Nevertheless, the naturalistic spirit and orientation of Peirce's work remains compelling and productive.

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